Sifuentes, J.
, Gimbutas, Z.
and Greengard, L.
(2015),
Randomized methods for rank-deficient linear systems, Electronic Transactions on Numerical Analysis, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=915064
(Accessed October 11, 2025)
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Randomized methods for rank-deficient linear systems
Published
Author(s)
Josef Sifuentes, , Leslie Greengard
Abstract
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without additional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix corresponding to a known eigenvalue. The method is based on elementary linear algebra combined with the observation that if the matrix is rank-k deficient, then a random rank k perturbation yields a nonsingular matrix with probability 1.Citation
Electronic Transactions on Numerical Analysis
Volume
44
Pub Type
Journals
Download Paper
Keywords
eigenvectors, integral equations, nullspace, null vectors, randomized algorithms, rank-deficient systems.
Citation
Issues
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Created February 12, 2015, Updated October 12, 2021